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Complex material behavior is represented by a single equation of product form.

Complex material behavior is represented by a single equation of product form to
account for interaction among the various
factors. The factors are selected by the
physics of the problem and the environment that the model is to represent. For
example, different factors will be required
for each to represent temperature, moisture, erosion, corrosion, etc. It is important
that the equation represent the physics of
the behavior in its entirety accurately.

The Multi-Factor Interaction Model
(MFIM) is used to evaluate the divot
weight (foam weight ejected) from the
external launch tanks. The multi-factor
has sufficient degrees of freedom to evaluate a large number of factors that may
contribute to the divot ejection. It also
accommodates all interactions by its product form. Each factor has an exponent
that satisfies only two points — the initial
and final points. The exponent describes
a monotonic path from the initial condition to the final. The exponent values are
selected so that the described path makes
sense in the absence of experimental
data. In the present investigation, the data
used were obtained by testing simulated
specimens in launching conditions.
Results show that the MFIM is an effective
method of describing the divot weight
ejected under the conditions investigated.

The problem lies in how to represent the
divot weight with a single equation. A unique
solution to this problem is a multi-factor
equation of product form. Each factor is of
the following form (1 – xi/xf)ei, where xi is
the initial value, usually at ambient conditions, xf the final value, and ei the exponent
that makes the curve represented unimodal
that meets the initial and final values. The
exponents are either evaluated by test data
or by technical judgment. A minor disadvantage may be the selection of exponents in
the absence of any empirical data. This form
has been used successfully in describing the
foam ejected in simulated space environmental conditions. Seven factors were
required to represent the ejected foam. The
exponents were evaluated by least squares
method from experimental data.

The equation is used and it can represent multiple factors in other problems as
well; for example, evaluation of fatigue
life, creep life, fracture toughness, and
structural fracture, as well as optimization
functions. The software is rather simplistic. Required inputs are initial value, final
value, and an exponent for each factor.
The number of factors is open-ended.
The value is updated as each factor is
evaluated. If a factor goes to zero, the previous value is used in the evaluation.

This work was done by Galib H. Abumeri
and Christos C. Chamis of Glenn Research
Center.

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